Configuration to reduce non-linear motion

ABSTRACT

Embodiments for modifying a spring mass configuration are disclosed that minimize the effects of unwanted nonlinear motion on a MEMS sensor. The modifications include any or any combination of providing a rigid element between rotating structures of the spring mass configuration, tuning a spring system between the rotating structures and coupling an electrical cancellation system to the rotating structures. In so doing unwanted nonlinear motion such as unwanted 2 nd  harmonic motion is minimized.

PRIORITY CLAIM

Under 35 U.S.C. 120, this application is a Continuation Application andclaims priority to U.S. patent application Ser. No. 15/814,373, filedNov. 15, 2017, entitled, “CONFIGURATION TO REDUCE NON-LINEAR MOTION,”which application is a Continuation Application of U.S. patentapplication Ser. No. 14/495,786, filed Sep. 24, 2014, entitled,“CONFIGURATION TO REDUCE NON-LINEAR MOTION,” which application claimsbenefit under 35 USC 119(e) of U.S. Provisional Patent Application No.61/929,838, filed on Jan. 21, 2014, entitled, “PERFORMANCE IMPROVEMENTSON 3-AXIS FRAME MICRO GYROSCOPES,” the entireties of which areincorporated herein by reference.

TECHNICAL FIELD

The present invention relates generally to angular velocity sensors andmore particularly relates to angular velocity sensors that includeguided mass systems.

BACKGROUND

Sensing of angular velocity is frequently performed using vibratory rategyroscopes. Vibratory rate gyroscopes broadly function by driving thesensor into a first motion and measuring a second motion of the sensorthat is responsive to both the first motion and the angular velocity tobe sensed.

Frequently, a mass, usually referred to as a proof mass, within thesensor is driven into oscillation by an actuator. Rotation of the sensorimparts a Coriolis force to the oscillating mass that is proportional tothe angular velocity (or rotation rate), and depends on the orientationof the angular velocity vector with respect to the velocity vector ofthe proof mass. The Coriolis force, the angular velocity vector, and theproof-mass velocity vector are mutually orthogonal. For example, aproof-mass moving in an X-direction within a sensor rotating about aY-axis experiences a Z directed Coriolis force. Similarly, a proof-massmoving in an X-direction within a sensor rotating about a Z-axisexperiences a Y directed Coriolis force. Finally, a proof-mass moving inan X-direction within a sensor rotating about the X-axis experiences noCoriolis force. Coriolis forces imparted to the proof-mass are usuallysensed indirectly by measuring motions within the sensor that areresponsive to the Coriolis forces.

Conventional gyroscopes that sense angular velocity about an in-planeaxis (i.e. X-axis or Y-axis) can be driven out-of-plane, and theCoriolis response is sensed in-plane or vice versa. Out-of-plane drivetends to be less efficient than in-plane drive, requires additionalfabrication steps, and is limited by nonlinearities. For example,driving the proof-mass out-of-plane might require a large vertical gapor a cavity underneath the proof-mass to provide sufficient room for theproof-mass to oscillate. Forming a cavity under the proof-mass requiresadditional fabrication steps and increases cost. Typically electrostaticactuators of the parallel-plate type are used to drive the proof-massout-of-plane. The actuators are formed between the proof-mass and thesubstrate. The electrostatic force depends on the gap between theproof-mass and the substrate. Because the proof-mass oscillatesout-of-plane, the electrostatic force is nonlinear which tends to limitthe device performance Additionally, the electrostatic force is reducedbecause of the requirement to have large vertical gaps or a cavity underthe proof-mass. Achieving large amplitude oscillation requires largeforce and that might require high-voltage actuation. Adding high-voltageactuation increases the fabrication cost and complexity of theintegrated circuits.

Furthermore a conventional multi-axis gyroscope might use multiplestructures that oscillate at independent frequencies to sense angularrates. Each structure requires a separate drive circuit to oscillate therespective proof-masses. Having more than one drive circuit increasescost and power consumption.

Accordingly, what is desired is to provide a system and method thatovercomes the above issues. The present invention addresses such a need.

SUMMARY

Embodiments for modifying a spring mass configuration are disclosed thatminimize the effects of unwanted nonlinear motion on aMicro-Electro-Mechanical Systems (MEMS) sensor. The modificationsinclude any or any combination of providing a rigid element betweenrotating structures of the spring mass configuration, tuning a springsystem between the rotating structures and coupling an electricalcancellation system to the rotating structures. In so doing unwantednonlinear motion such as unwanted 2 harmonic motion is minimized

In an aspect, MEMS sensor is disclosed. The MEMS sensor includes a firstand second rotating arm. The first and second rotating arms are coupledto each other and the first and second rotating arms are configured tocounter rotate when driven into oscillation. The MEMS sensor alsoincludes at least one travelling system. The at least one travellingsystem is coupled to the first and second rotating arms. Finally, theMEMS sensor includes at least one actuator for driving the at least onetravelling system into oscillation. The at least one travelling systemmoves in a first direction when driven into oscillation.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 illustrates four different spring-mass configurations 10, 11, 12and 13, respectively.

FIGS. 2A and 2B illustrate an embodiment of a single axis gyroscopecomprising a guided mass system.

FIG. 3 illustrates an embodiment of a single axis gyroscope comprising aguided mass system in accordance with the present invention.

FIG. 4 shows a modification of a guided mass system to eliminate the 2ndharmonic component of the drive motion.

FIG. 5 illustrates another embodiment of a single axis gyroscopecomprising a balanced guided mass system in accordance with anembodiment of the present invention.

FIGS. 6a and 6b illustrates an embodiment of a tri-axis gyroscopecomprising a multiple guided mass system in accordance with the presentinvention.

DETAILED DESCRIPTION

The present invention relates generally to angular velocity sensors andmore particularly relates to angular velocity sensors that includeguided mass systems. The following description is presented to enableone of ordinary skill in the art to make and use the invention and isprovided in the context of a patent application and its requirements.Various modifications to the preferred embodiments and the genericprinciples and features described herein will be readily apparent tothose skilled in the art. Thus, the present invention is not intended tobe limited to the embodiments shown, but is to be accorded the widestscope consistent with the principles and features described herein.

Micro-Electro-Mechanical Systems (MEMS) refers to a class of devicesfabricated using semiconductor-like processes and exhibiting mechanicalcharacteristics such as the ability to move or deform. MEMS often, butnot always, interact with electrical signals. A MEMS device may refer toa semiconductor device implemented as a Microelectromechanical system. AMEMS device includes mechanical elements and optionally includeselectronics for sensing. MEMS devices include but are not limited togyroscopes, accelerometers, magnetometers, and pressure sensors.

FIG. 1 illustrates four different spring-mass configurations 10, 11, 12and 13, that could be utilized in a MEMS sensor, respectively. A firstspring-mass configuration 10 includes a spring-mass system 10A. Thespring mass system 10A includes a lever arm 20A, a proof mass 30A, alinear spring 40A, and a hinge 50A attached to a stable point 60A. Theproof mass, 30A, in the spring mass system 10A has three degrees offreedom. The proof mass 30A can rotate by an angle θ about an axispassing from the center of the hinge 50A and normal to a first plane inthis embodiment, the XY plane, and it can translate in X and Y directionas it rotates in the X-Y plane. Although it is not shown in FIG. 1 indetail, hinge 50A has a finite translational compliance, and linearspring 40A has a finite rotational compliance. If it is assumed that thelength of the spring 40A is negligible and the length of the lever arm20A is L. The X direction motion of the mass 30A is given by theequation:

X _(d) =Lsin(θ)≈Lθ  (Eq-1)

where X_(d) is the x-direction translation motion of the proof mass 30A.Since the motion of the proof mass 30A is rotational, there is also Ydirection component of the motion of the proof mass 30A which can berepresented as in the equation given below:

$\begin{matrix}{Y_{d} = {{L\left( {1 - {\cos (\theta)}} \right)} \approx {L\frac{\theta^{2}}{2}}}} & \left( {{Eq}\text{-}2} \right)\end{matrix}$

where Y_(d) is the Y-direction translation motion of the proof-mass.

If the mass 30A is driven at a frequency cod which is named as drivefrequency, where the drive frequency can be the natural frequency of thespring mass system 10A, the governing equation for the rotational drivemotion of the mass 30A can be given as:

θ=|θ|sin(ω_(d) t)   (Eq-3)

Then X-direction motion of the proof mass 30A at the drive frequency canbe given as:

X _(d) ≈L|θ|sin(ω_(d) t)   (Eq-4)

Y direction motion of the proof mass 30A can be represented by thefollowing equation:

$\begin{matrix}{{Y_{d} \approx {L\frac{\left| \theta  \middle| {}_{2}{\sin^{2}\left( {\omega_{d}t} \right)} \right.}{2}}} = \left. L \middle| \theta  \middle| {}_{2}\frac{1 - {\cos \left( {2\omega_{d}t} \right)}}{4} \right.} & \left( {{Eq}\text{-}5} \right)\end{matrix}$

As it can be seen in the equations 4 and 5, the Y direction motion ofthe mass 30A is at two times the drive frequency. This behavior is dueto the non-linearity of the rotational movement of the proof mass 30A.If the mass is driven in the X direction with the use of a lever arm 20Aat the drive frequency, there is always a Y direction vibration which isat two times the drive frequency, which is referred to as 2^(nd)Harmonic vibration.

The 2^(nd) Harmonic vibration can be non-ideal for MEMS sensors that aredriven in one direction and the sensing motion is in-plane andorthogonal to the drive direction. As an example, if the X direction isthe drive direction and the sensing direction is the Y direction, anerroneous signal in Y direction with a frequency that is two times thedrive frequency is generated by the nonlinear motion of the lever arms.So, for those cases, it is needed to eliminate the Y direction componentof the nonlinear motion by the use of specific structures and elementswhich may be added to the spring-mass system 10A. To describe the issueswith a guided mass configuration 10, refer now to the followingdiscussion in conjunction with the accompanying figures.

FIG. 2A illustrates an embodiment of a single axis gyroscope comprisinga guided mass system 500. The guided mass system 500 is disposed in anX-Y plane parallel to a substrate 101 and comprises a guided mass system100 coupled to a yaw proof mass 518 a. The guided mass system 100includes guiding arms 104 a and 104 b that are flexibly coupled viasprings 108 a and 108 b to the substrate 101 via at least one anchoringpoint 106 a. The two guiding arms 104 a and 104 b are flexibly coupledto one proof-mass 102 a via springs 103 a and 103 b. The yaw proof mass518 a is flexibly connected to the proof mass 102 a via yaw-springs 520a-520 d.

The proof mass 102 a and yaw proof mass 518 a, guiding arms 104 a and104 b, anchoring point 106 a, and springs 103 a, 103 b, 108 a, and 108 bform a planar four-bar linkage. The springs 103 a, 103 b, 108 a, and 108b are compliant in-plane about an axis in the Z-direction so that eachguiding arm 104 a and 104 b can rotate in-plane while the proof-mass 102a translates in an X-direction, as shown in FIG. 2B. Yaw-springs 520a-520 d are stiff in the X-direction such that when the guided masssystem 100 translates in the X-direction, the yaw proof-mass 518 a alsotranslates with the proof mass 102 a.

Electrostatic actuators, such as comb drives 109 a and 109 b, areconnected to the proof mass 102 a to drive the guided mass system 100.In this embodiment, two electrostatic actuators are utilized.

However, one of ordinary skill in the art readily recognizes that oneelectrostatic actuator can be provided and the use of one electrostaticactuator would be within the spirit and scope of the present invention.In addition, although electrostatic actuators will be describedthroughout this specification as the actuators being used to drive theguided mass systems, one of ordinary skill in the art recognizes that avariety of actuators could be utilized for this function and that usewould be within the spirit and scope of the present invention. Forexample, the actuators could be piezoelectric, thermal orelectromagnetic or the like.

The guided mass system 500 can be driven at a drive frequency by asingle drive circuit coupled to the actuators 109 a and 109 b. The drivefrequency can be a resonant frequency of the guided mass system 500.When the guided mass system 500 is driven, the guiding arms 104 a and104 b rotate in-plane and the proof-mass 102 a and yaw proof mass 518 atranslate in-plane in the X-direction.

Angular velocity about a yaw-input axis in the Z-direction will cause aCoriolis force to act on the yaw proof-mass 518 a in the Y-directionresulting in motion of the yaw proof-mass 518 a in the Y-direction. Acapacitive electrode 522 a is used to sense the motion of the yawproof-mass 518 a in the Y-direction which provides a measure of theangular velocity about the yaw-input axis.

A variety of types of transducers could be utilized in a system andmethod in accordance with the present invention. For example, instead ofusing the capacitive electrode 522 a, one can also use a piezoelectricor optical or the like transducer and its use would be within the spiritand scope of the present invention.

The guided mass system 500 can be simply represented by the spring masssystem 10A that is shown in FIG. 1. The lever arms 104 a-104 b aresimilar to the lever arm 20A, the springs 103 a-103 b, 108 a-108 b and520 a-520 d of the guided mass system 500 are compliant in the Ydirection. As a result, the spring 40A can be a representation of ydirection compliance of the springs 103 a-103 b, 108 a-108 b and 520a-520 d. The proof mass 102 a and the yaw proof-mass 518 a are attachedto the springs 103 a-103 b and 520 a-520 d, respectively, as the proofmass 30A is attached to the spring 40A. Finally, in-plane rotationalcompliance of the springs 108 a-108 b that are attached to the anchor106 a can be represented by the hinge 50A and the stable point 60A.

As it is shown in FIG. 2B, the motion of the center of mass of proofmass 102 a has a non-linear motion. When the proof mass 102 a and yawproof-mass 518 a are driven in the X direction, there is also a motionin Y direction that is at two times the drive frequency which is due tothe nonlinearity of the drive motion as it has been explained in FIG. 1for the spring-mass configuration 10. The motion at two times the drivefrequency can also be called the 2^(nd) harmonic motion of the guidedmass system 500. In the single axis gyroscope shown in FIG. 2A, the2^(nd) Harmonic motion is sensed by the capacitive electrode 522 a as anerroneous signal and it may corrupt the readings or saturate the frontend electronics.

In certain conditions, guided mass system 500 can also be used as a dualaxis gyroscope. If the springs 108 a and 108 b are compliant about afirst roll-sense axis in the X-direction then the guiding arms 104 a and104 b can rotate out-of-plane, whereby out-of-plane rotation of theguiding arms 104 a and 104 b causes the proof mass 102 a and the yawproof mass 518 a move out-of-plane with the guiding arms 104 a and 104b.

While the guided mass system 500 is driven, an angular velocity about aroll-input axis in the Y-direction that is in the plane of the substrateand orthogonal to the X-direction will cause a Coriolis force to act onthe proof-mass 102 a and the yaw proof-mass 518 a in the Z-direction.The Coriolis force causes the guided mass system 500 to rotateout-of-plane about the first roll-sense axis. When the guided masssystem 500 rotates out-of-plane, the guiding arms 104 a and 104 b andthe proof mass 102 a and yaw proof mass 518 a rotate out-of-plane aboutthe first roll-sense axis. The amplitude of the rotation of the guidedmass system 500 is proportional to the angular velocity about theroll-input axis.

A capacitive electrode 112 a under the proof mass 102 a is used todetect the rotation of the guided mass system 500 about the firstroll-sense axis. The rotation provides a measure of the angular velocityabout the roll-input axis. A variety of types of transducers could beutilized in the present invention. For example, the capacitive electrode112 a could be also piezoelectric or optical or the like and its usewould be within the spirit and scope of the present invention.

The guided mass system 500 of FIG. 2A can be modified to eliminate the2^(nd) harmonic motion by using the methods that are introduced in oneor more of the spring mass configurations 11, 12 and 13 shown in FIG. 1.To describe these configurations and methods in more detail refer now tothe following description in conjunction with the accompanying Figures.

A second spring-mass configuration 11 is shown in FIG. 1 that hascomponents similar to the spring-mass configuration 10. Spring massconfiguration 11 includes two spring mass systems 11A-11B. Each of thetwo spring mass systems 11A-11B comprise lever arms 21A-21B, and atraveling system 101A comprising traveling masses 31A-31B and connectionelement 21, linear springs 41A-41B, hinges 51A-51B attached to stablepoints 61A-61B.

The difference between spring-mass configuration 11 and the spring massconfiguration 10 is connection element 21 that connects two spring-masssystems 11A and 11B. In the spring-mass configuration 11, while twospring-mass systems 11A-11B are operated side by side, they are alsoconnected by the connection element 21. Both 11A and 11B move in thesame X direction during the drive operation. But, the Y direction motionof 11A and 11B are opposing each other. If those two spring-mass systems11A-11B are rigidly connected by the connection element 21, then thespring elements 41A and 41B stretches in opposite directions toaccommodate the nonlinear motion due to the rotation of the lever arms21A and 21B. As a result of the compensation of the 2^(nd) harmonicmotion by the spring elements 41A and 41B, the net motion on thetraveling masses 31A and 31B in Y direction becomes zero. Consequently,the traveling masses 31A and 31B can be restricted to move only in the xdirection by eliminating the unwanted 2^(nd) harmonic Y directionmotion.

Spring mass configuration 12 includes two spring mass systems 12A-12Bwhich comprise lever arms 22A-22B, a traveling system 101B comprisingtraveling masses 32A-32B and spring element 22, linear springs 42A-42B,and hinges 52A-52B attached to stable points 62A-62B. In contrast tospring mass configuration element 10, the springs 42A and 42B havedifferent spring stiffness values. Moreover, an additional component ofspring-mass configuration 12 compared to spring mass configuration 10 isthe spring element 22 coupled between traveling masses 32A and 32B.Spring element 22 is used to eliminate the unwanted 2nd harmonic Ydirection motion of the traveling masses 32A or 32B. Compliance of thespring 22 can be designed such a way that the 2nd harmonic motion of oneof the spring-mass system 12B can be used to compensate for the 2^(nd)harmonic motion of the other spring-mass system 12A, or vice versa. Forexample, by ensuring that the spring stiffness the spring 42B is equalto the combined stiffness of the spring 22 and the spring 42A, the2^(nd) harmonic motion of the traveling mass 32A can be eliminated dueto the balance of the opposing forces as in the spring massconfiguration 11. In this scenario, traveling mass 32B would still havean unwanted 2^(nd) harmonic motion.

A third modification to the spring-mass configuration 10 is shown as thespring-mass configuration 13. Spring mass configuration 13 includes twospring-mass systems 13A-13B which are composed of lever arms 23A-23B,and a traveling system 1010 comprising traveling masses 33A-33B, springelement 23, transducers 73A-73B and 74A-74B, linear springs 43A-43B, andhinges 53A-53B attached to stable points 63A-63B.

The additional components of spring-mass configuration 13 compared tospring mass configuration 10 are spring element 23 and transducers73A-73B and 74A-74B. By coupling two spring mass systems 13A and 13B,both of the traveling masses 33A and 33B can be resonated in the drivedirection at a natural drive frequency. Furthermore, by coupling thetraveling masses 33A and 33B using the spring 23, the proof masses 33Aand 33B can also resonate in the Y direction at another naturalfrequency. Transducers 73A-73B and 74A-74B are used to sense the motionof the traveling masses 33A-33B in Y direction. Transducers in anembodiment could be capacitive, piezoresistive or the like, although oneof ordinary skill in the art readily recognizes that the transducerscould a variety of types and that would be within the spirit and scopeof the present invention.

The sensing direction of the transducers 73A-73B and 74A-74B can beselected such a way that the 2^(nd) harmonic component of the drivemotion in Y direction can be rejected, but the signals that are usefulcan be preserved. As an example, in the spring-mass configuration 13, ifit is assumed that the common mode motion in the Y direction is thesensor response, as in the case of a yaw gyroscope undergoing Z-axisrotation, the Y direction 2^(nd) harmonic motion is rejected since theelectrodes cancels the opposing (differential) motions in Y direction.

The spring-mass configuration 13 is given as an example for theelectrical cancellation of unwanted 2^(nd) Harmonic motion in Ydirection; however, there may be different sensing and rejection schemesof transducers, depending on the proof mass and electrodeconfigurations. In other configurations, the common mode motion can berejected but the differential motion can be detected.

The following description will describe different guided mass systemsthat incorporate on or more of the spring mass configurations 11-14described above.

FIG. 3 illustrates an embodiment of a single axis gyroscope comprising aguided mass system in accordance with the present invention. The guidedmass system 600 is disposed in an X-Y plane. The guided mass system 600includes guiding arms 104 a, 104 b, 104 c and 104 d that are flexiblycoupled via springs 108 a, 108 b, 108 c and 108 d to the substrate 100via the anchoring points 106 a and 106 b. Four guiding arms 104 a, 104b, 104 c and 104 d are flexibly coupled to one traveling mass 105 viasprings 103 a, 103 b, 103 c and 103 d.

Each spring 103 a-103 d, 108 a-108 d is compliant in-plane about an axisin the Z-direction so that each guiding arm 104 a-104 b and 104 c-104 dcan rotate anti-phase in the plane while the traveling mass 105translates in an X-direction. The yaw proof-masses 518 a and 518 b areflexibly connected to the traveling mass 105 via yaw-springs 520 a-520 dand 520 e-520 h, respectively. The guided mass system 600 can be drivenat a drive frequency by a single drive circuit coupled to the actuators109 a-109 d. The drive frequency can be a resonant frequency of theguided mass system 600. When the guided mass system 600 is driven, theguiding arms 104 a-104 b and 104 c-104 d rotate anti-phase in-plane andthe traveling-mass 105 translates in-plane in the X-direction.Yaw-springs 520 a-520 d and 520 e-520 h are stiff in the X-directionsuch that when the guided mass system is driven, the yaw proof-masses518 a-b also translate with the traveling mass 105 in the X-direction.

Angular velocity about a yaw-input axis in the Z-direction will cause aCoriolis force to act on the yaw proof-masses 518 a-518 b in theY-direction resulting in a common mode motion of the yaw proof-masses518 a and 518 b. The capacitive electrodes 522 a and 522 b are used tosense the motion of the yaw proof-masses 518 a and 518 b in theY-direction which provides a measure of the angular velocity about theyaw-input axis.

The configuration shown in FIG. 3 can be represented as the spring massconfiguration 11 of FIG. 1. As in the spring mass configuration 11,guided mass system 600 eliminates the second harmonic motion bycombining two guided mass systems by a rigid traveling mass 105. Sincethe motion of the lever arms 104 a-104 b and 104 c-104 d are anti-phasewith respect to each other, the travelling mass 105 that is connected tothe lever arms 104 a-104 d balances the opposing 2^(nd) harmonic motionand eliminates the unwanted non-linear component of the drive motion,and the y direction compliance of the spring elements 108 a-108 b, 103a-103 b and 108 c-108 d, 103 c-103 d accommodates the 2^(nd) Harmonicmotion by stretching in y direction similar to the spring massconfiguration 12.

In certain conditions, guided mass system 500 can also be used as a dualaxis gyroscope. If we assume that the springs 108 a-108 b and 108 c-108d are compliant about a first and second roll-sense axis, respectively,where the first and second roll sense axes are parallel to each otherand they are in the X-direction, then the guiding arms 104 a-104 b and104 c-104 d can rotate anti-phase out-of-plane, whereby out-of-planerotation of the guiding arms 104 a-104 d causes the traveling mass 105to move out-of-plane with the guiding arms 104 a-104 d.

Angular velocity about a roll-input axis in the Y-direction that is inthe plane of the substrate and orthogonal to the X-direction will causea Coriolis force to act on the traveling mass 105 in the Z-direction.The Coriolis force causes the lever arms 104 a-104 b and lever arms 104c-104 d rotate anti-phase out-of-plane about the first and secondroll-sense axes and the traveling mass 105 moves in the Z direction. Theamplitude of the motion of the roll-travelling mass 105 is proportionalto the angular velocity about the roll-input axis. A capacitiveelectrode 112 a under the traveling mass 105 is used to detect themotion of the proof-mass. This motion provides a measure of the angularvelocity about the roll-input axis.

FIG. 4 illustrates a second embodiment of a single axis gyroscopecomprising a guided mass system 700 in accordance with the presentinvention which minimizes a 2nd Harmonic component of the drive motion.

The guided mass system 700 comprises two guided mass systems 700A and700B, which are same as the guided mass system 500. The proof masses 102a and 102 b, consequently two guided mass systems 700A and 700B, areconnected by a coupling spring 151. The yaw proof-masses 518 a and 518 bare flexibly connected to the proof-masses 102 a and 102 b,respectively. The coupling spring 151 is torsionally compliant about anaxis in the X-direction so that the symmetric guided mass systems 700Aand 700B can rotate anti-phase out-of-plane about the first and secondroll-sense axes. The coupling spring 151 is stiff in the Z-directionwhich prevents the guided mass systems 700A and 700B from rotatingin-phase out-of-plane.

The coupling spring 151 is stiff in the X-direction such that theproof-mass 102 a and 102 b move together in the X-direction. In this waythe two guided mass systems 700A and 700B are driven together at a drivefrequency by a single drive circuit coupled to the actuators 109 a-109d.

The configuration given in FIG. 4 can be represented by the spring massconfiguration 13 given in FIG. 1. As in the spring mass configuration13, two guided mass systems 700A and 700B are connected by a couplingspring 151, so that the proof masses 102 a-102 b and 518 a-518 b canalso resonate in the Y direction at a certain natural frequency.Capacitive electrodes 522 a and 522 b are used to sense the motion ofthe proof-masses 518 a and 518 b in Y direction, respectively. Thesensitive direction of the capacitive electrodes 522 a-522 b can beselected such a way that the 2^(nd) harmonic motion in the Y directionis rejected but the Coriolis motion in the Y direction is detected.

In the guided mass system 700, the proof masses 518 a and 518 b move inthe same direction in the drive motion. Hence, an angular velocity abouta yaw-input axis in the Z-direction will impart a Coriolis force on theyaw proof-masses 518 a-b in the same Y-direction (common mode motion).

Due to the placement of the electrodes 522 a and 522 b in the guidedmass system 700, the capacitance of the electrodes 522 a and 522 bchanges in opposite directions while the proof masses 518 a-518 b movein the same direction.

If the capacitance change on the electrodes is subtracted from eachother, the common mode Coriolis response of the proof masses 518 a and518 b is able to be detected.

On the other hand, the 2^(nd) harmonic motions of the proof masses 518a-518 b in the Y direction are in opposite directions, because theguiding arms 104 a-104 b and 104 c-104 d are rotating around oppositedirections. Consequently, the 2^(nd) harmonic motion of the proof masses518 a-518 b will be cancelled due to the configuration of the electrodes522 a-522 b.

FIG. 5 illustrates another embodiment of a single axis gyroscopecomprising a balanced guided mass system 1000 in accordance with anembodiment of the present invention. The guided mass system 1000includes two symmetric guided mass systems 900 a and 900 b which areconnected by a coupling spring 302. However, the coupling between theguided mass systems 900 a and 900 b doesn't have to be only a singlecoupling spring 302; the coupling may include various springs andspring-mass systems.

The two symmetric guided mass systems 900 a and 900 b are arranged sothat the proof-masses 102 a-102 d all move in the X-direction. Hence,the two guided mass systems 900 a and 900 b are driven together at adrive frequency by a single drive circuit coupled to the actuators 109a-109 h.

In the drive motion of the guided mass system 1000, the proof-masses 102b and 102 c move together in the same X-direction, since the couplingspring 302 is stiff in the X-direction. On the other hand, the proofmasses 102 a and 102 d move in the opposite X-direction compared to theproof masses 102 b and 102 c.

Angular velocity about the yaw-input axis will cause Coriolis forces toact on the yaw proof-masses 518 a-518 d resulting in motion of the yawproof-masses 518 a-518 d along the Y-direction. The amplitude of themotions of the yaw proof-masses 518 a-518 d is proportional to theangular velocity about the yaw-input axis.

The schematic provided in FIG. 5 is a different embodiment of thespring-mass configuration 13 shown in FIG. 1. The balanced guided masssystem 1000 eliminates the unwanted 2nd harmonic motion of the yaw proofmasses 518 a-518 d by electrical cancellation.

Due to the nature of the drive motion explained above, the impartedCoriolis forces on the proof masses 518 a and 518 d are in the oppositedirection of the imparted Coriolis forces on the proof masses 518 a and518 d. In other words, the Coriolis response motion of the proof masses518 b and 518 c vs. the proof masses 518 a and 518 d are differential.In order to detect the differential motion effectively within the givenelectrode placements in FIG. 5, the capacitance change of the electrodes522 a and 522 b due to the Coriolis motion of the proof masses 518 a-518b can be summed up. The capacitance change of the electrodes 522 c and522 d can also be summed up. Moreover, the detected capacitance changefrom the electrode pair 522 c-522 d can be subtracted from the detectedcapacitance change of the electrode pair 522 a-522 b. As a result of theelectrode configuration, the Coriolis motion is detected.

The 2nd harmonic motion direction of the each proof mass 518 a-518 d isillustrated by the arrows 541 a-541 d which are shown side by side bythe arrows 540 a-540 d that are showing the Coriolis force direction ofthe proof masses 518 a-518 d. The given arrow configuration shows thatthe Coriolis force and the 2nd harmonic motion are in the same directionfor the guided mass system 900 b but they are in the opposite directionsfor the guided mass system 900 a. As a result, the 2nd harmonic motionwill be cancelled due to the electrode scheme given above.

The balanced guided mass system 1000 can also be used as a dual axisgyroscope with a condition where the symmetric guided mass system 900 ais able to rotate out-of-plane about a first roll-sense axis and thesymmetric guided mass system 900 b is able to rotate out-of-plane abouta second roll-sense axis in-plane and parallel to the first roll-senseaxis.

The coupling spring 302 is connected to proof-masses 102 b and 102 c.The coupling spring 302 is torsionally compliant about an axis in theX-direction so that the symmetric guided mass systems 900 a and 900 bcan rotate anti-phase out-of-plane about the first and second roll-senseaxes. The coupling spring 302 is stiff in the Z-direction which preventsthe symmetric guided mass systems 900 a and 900 b from rotating in-phaseout-of-plane.

Angular velocity about the roll-input axis will cause Coriolis forces toact on the proof-masses 102 a-102 d in the Z-direction. The Coriolisforces cause the symmetric guided mass systems 900 a and 900 b to rotateanti-phase out-of-plane about the first and second roll-sense axes. Theamplitudes of the rotations of the symmetric guided mass systems 900 aand 900 b are proportional to the angular velocity. Capacitiveelectrodes 112 a-112 c under the proof masses 102 a-102 d are used todetect the rotations of the symmetric guided mass systems 900 a and 900b.

FIG. 6a illustrates an embodiment of a tri-axis gyroscope comprising amultiple guided mass system 1100 in accordance with the presentinvention. The multiple guided mass system 1100 includes two guided masssystems 500 a and 500 b coupled to a guided mass system 800 by couplingsprings 302 a and 302 b, respectively.

The guided mass systems 500 a, 500 b and 800 are arranged so that yawproof-masses 518 a and 518 b coupled to roll proof masses 102 a-102 dall move anti-phase in the X-direction, the pitch proof-mass 650 arotates about an axis in the Z-direction. The guided mass system 500 arotates out-of-plane about a first roll-sense axis. The symmetric guidedmass system 800 rotates out-of-plane about a second roll-sense axisparallel to the first roll-sense axis. The guided mass system 500 brotates out-of-plane about a third roll-sense axis parallel to the firstand second roll-sense axes. The first coupling spring 302 a is connectedto proof-masses 102 a and 102 b. The coupling spring 302 a is stiff inthe X-direction such that proof-mass 102 a and 102 b move together inthe X-direction. The second coupling spring 302 b is connected toproof-masses 102 c and 102 d. The coupling spring 302 b is stiff in theX-direction such that proof-mass 102 c and 102 d move together in theX-direction. In this way the guided mass systems 500 a, 500 b, and 800are driven together at a drive frequency by a single drive circuitcoupled to the actuators 109 a-109 h. Moreover, as it can be seen inFIG. 6a , folded flexures are used as coupling springs 302 a-b.

The coupling spring 302 a is torsionally compliant about an axis in theX-direction so that the guided mass systems 500 a and 800 can rotateout-of-plane about the first and second roll-sense axes anti-phase. Thecoupling spring 302 a prevents the symmetric guided mass systems 500 aand 800 from rotating out-of-plane in-phase.

The coupling spring 302 b is also torsionally compliant about an axis inthe X-direction so that the guided mass systems 500 b and 800 can rotateout-of-plane about the second and third roll-sense axes anti-phase. Thecoupling spring 302 b prevents the symmetric guided mass systems 500 band 800 from rotating out-of-plane in-phase.

Angular velocity about the pitch-input axis will cause Coriolis forcesto act on the pitch proof-mass 650 a resulting in a torque that rotatesthe pitch proof-mass 650 a about the pitch-sense axis. The amplitude ofthe rotation of the pitch proof-mass 650 a is proportional to theangular velocity about the pitch-input axis. The capacitive electrodes660 a and 660 b are disposed on opposite sides along the X-directionunder the pitch proof-mass 650 a and detect the rotation of the pitchproof-mass about the pitch-sense axis. The rotation provides a measureof the angular velocity about the pitch-input axis.

Angular velocity about the roll-input axis will cause Coriolis forces toact on the proof-masses 102 a and 102 b in a Z-direction and onproof-masses 102 c and 102 d in the opposite Z-direction. The Coriolisforces cause the guided mass systems 500 a, 800, and 500 b to rotateout-of-plane about the first, second, and third roll-sense axisrespectively. The capacitive electrode 112 b under the proof masses 102a and 102 b and the capacitive electrode 112 a under the proof masses102 c and 102 d are used to detect the rotation of the guided masssystem 1100. This rotation provides a measure of the angular velocityabout the roll-input axis.

Angular velocity about the yaw-input axis will cause Coriolis forces toact on the yaw proof-masses 518 a and 518 b resulting in motion of theyaw proof-masses 518 a and 518 b anti-phase along the Y-direction. Theamplitude of the motion of the yaw proof-masses along the Y-direction isproportional to the angular velocity. The capacitive electrodes 522 aand 522 b are used to sense the motion of the respective yaw proofmasses 518 a and 518 b along the Y-direction.

The multiple guided mass system 1100 of FIG. 6a can be represented bythe spring mass configuration 12 shown in FIG. 1. The spring-mass system12A is a representation of one of the guided mass systems 500 a or 500b, and the spring-mass system 12B is a representation of the guided masssystem 800.

The springs 103 c-103 f and 108 c-108 d are compliant in y direction andtheir compliance can be modeled by an equivalent spring as 42B, which isgiven in spring mass system configuration 12 in FIG. 1. In the guidedmass system 500 a, the springs 108 a-108 b, 103 g-103 h and 520 a-520 dcan be modeled by the spring 42A. The coupling spring 302 a thatconnects 500 a and 800 can be modeled as spring 22. The lever arms 104c-104 d can be modeled as the lever arm 22B, and the lever arms 104a-104 b can be represented as 22A.

Y direction spring stiffness of the guided mass system 800 is muchhigher than the y direction spring stiffness of the guided mass system500 a or 500 b. The reason is that the springs sets 103 c-103 d and 103e-103 f have been equally spread in the guided mass system 800, and alsothe springs 652 a and 652 b are very stiff in Y direction.

By using the same 2nd harmonic motion elimination illustrated byspring-mass configuration 12 of FIG. 1, the y direction spring stiffnessof the springs 103 c-103 f, 108 c-108 d, and 652 a-652 b can be madeequal to the sum of the spring stiffness of the coupling spring 302 aand the springs 108 a-108 b, 103 g-103 h and 520 a-520 d. As a result,the net nonlinear motion in y direction of the yaw-proof masses 518a-518 b can be eliminated by the help of the balance of the opposingforces in y direction. As it was mentioned before a folded flexure isused as coupling spring 302 a. The main benefit of using a foldedflexure is to increase the y direction translational stiffness ofcoupling spring 302 a, while maintaining its out-of plane torsionalcompliance within the given area. Although, a two-fold folded flexure isused in embodiment 1100, folded flexure with many folds can also be usedto increase the y direction translational stiffness.

FIG. 6b illustrates another embodiment of a tri-axis gyroscopecomprising a multiple guided mass system 1110 in accordance with thepresent invention. Multiple guided mass system is same as multipleguided mass system 1100, except new coupling springs 303 a and 303 b areadded in between proof masses 102 a-b and 102 c-d respectively. Mainbenefit of adding springs 303 a and 303 b in multiple guided system 1110is to increase the y direction translational stiffness. Moreover,springs 303 a-b improves x direction stiffness. As a result, rigidity ofmultiple guided mass system 1110 during the drive motion increases andproof masses 102 a-b and 102 c-d move together in the x direction.

Embodiments for modifying a spring mass configuration are disclosed thatminimize the effects of unwanted nonlinear motion on a MEMS sensor. Themodifications include any or any combination of providing a rigidelement between rotating structures of the spring mass configuration,tuning a spring system between the rotating structures and coupling anelectrical cancellation system to the rotating structures. In so doingunwanted nonlinear motion such as unwanted 2^(nd) harmonic motion isminimized.

Although the present invention has been described in accordance with theembodiments shown, one of ordinary skill in the art will readilyrecognize that there could be variations to the embodiments and thosevariations would be within the spirit and scope of the presentinvention. Accordingly, many modifications may be made by one ofordinary skill in the art without departing from the spirit and scope ofthe present invention.

1. A Micro-Electro-Mechanical Systems (MEMS) sensor comprising; firstand second rotating arms, wherein the first and second rotating arms arecoupled to each other and the first and second rotating arms areconfigured to counter rotate when driven into oscillation in a firstdirection, wherein the first rotating arm is coupled to a first anchoron a substrate by a first flexible element, wherein the second rotatingarm is coupled to a second anchor on the substrate by a second flexibleelement; at least one travelling system comprising at least a firsttravelling mass and a second travelling mass and at least one proofmass, wherein the first travelling mass is coupled to the first rotatingarm by a third flexible element and the second travelling mass iscoupled to the second rotating arm by a fourth flexible element, whereinthe at least the first travelling mass and the second travelling massare coupled to each other by a fifth flexible element, wherein the fifthflexible element is compliant in a direction orthogonal to the firstdirection, wherein the second travelling mass is coupled to the at leastone proof mass, wherein the first travelling mass moves in a non-linearmotion orthogonal to the first direction and the at least one proof massand the second travelling mass move in a linear translation in the firstdirection, when driven into oscillation; and at least one actuator fordriving the at least one travelling system into oscillation.
 2. The MEMSsensor of claim 1, wherein the at least one proof mass and the secondtravelling mass move in a plane parallel to the substrate.
 3. The MEMSsensor of claim 1, wherein the first and second rotating arms arecoupled to an anchor system, comprising the first anchor and the secondanchor, on the substrate by a set of flexible elements, wherein the setof flexible elements comprise at least the first, the second, the third,the fourth, and the fifth flexible elements, and wherein the set offlexible elements are balanced to minimize transmission of thenon-linear motion orthogonal to the first direction to the at least oneproof mass and the second travelling mass.
 4. The MEMS sensor of claim1, wherein a first subset comprising the first, the third, and the fifthflexible elements and a second subset comprising the second and fourthflexible elements are balanced with respect to forces in the directionorthogonal to the first direction.
 5. (canceled)
 6. The MEMS sensor ofclaim 5, further comprising: a plurality of transducers configured tosense motions of at least a portion of at least one of the at least oneproof mass, the first travelling mass, or the second travelling mass.7-9. (canceled)
 10. The MEMS sensor of claim 6, wherein at least aportion of the first travelling system is configured to allow anout-of-plane rotation of the at least the portion of the firsttravelling system about a roll axis that is in plane with and orthogonalto the first direction.
 11. The MEMS sensor of claim 10, wherein theplurality of transducers are further configured to sense at least aportion of the out-of-plane rotation of the at least the portion of thefirst travelling system.
 12. The MEMS sensor of claim 10, wherein thefifth flexible element system is configured to allow the out-of-planerotation of the at least the portion of the first travelling system. 13.The MEMS sensor of claim 10, wherein the fifth flexible element systemis torsionally compliant about an axis parallel to the first directionto allow the out-of-plane rotation of the at least the portion of thefirst travelling system to be anti-phase with the oscillation. 14-16.(canceled)
 17. The MEMS sensor of claim 6, wherein the plurality oftransducers comprises at least one of a capacitive transducer, anoptical transducer, or a piezoelectric transducer.
 18. The MEMS sensorof claim 1, wherein the first and second rotating arms are configured toallow rotation of the first and second rotating arms in plane with andorthogonal to the first direction.
 19. The MEMS sensor of claim 1,wherein the fifth flexible element comprises a folded spring.
 20. TheMEMS sensor of claim 19, wherein the fifth flexible element comprises atleast the folded spring and at least one of another folded spring,another proof mass, or a rigid coupling element. 21-22. (canceled) 23.The MEMS sensor of claim 1, wherein at least one of the first, thesecond, the third, the fourth, or the fifth flexible element comprisesat least one folded flexure.
 24. The MEMS sensor of claim 23, whereinthe at least one of the first, the second, the third, the fourth, or thefifth flexible element comprises a plurality of springs comprisingfolded flexures.